The present invention concerns mechanical controls that, during the operation of an internal combustion engine continuously vary the strokes of individual valves and groups of valves from maximally open to constantly closed, while simultaneously varying how long the valve or valves remain open. The valves are actuated by rocker levers that are in turn driven by subsidiary rocker levers, or by tilting or angled levers. The particular positioning of the subsidiary rocker. tilting, or angled levers dictates the length and duration of the stroke. With the exception of one set, the valve-stroke controls allow actuation of the valves in the lower engine speed ranges. In accordance with manufacturers' specifications, once a shorter stroke has been selected, a considerably more acute angle of rotation for the open range of the valves and an angle even more acute in relation to the angle of rotation associated with valve opening will be available for the procedure of opening and closing the valves.